Disclosure Risk from Homogeneity Attack in Differentially Private Release of Frequency Distribution

Differential privacy (DP) provides a robust model to achieve privacy guarantees in released information. We examine the robustness of the protection against homogeneity attack (HA) in multi-dimensional frequency distributions sanitized via DP randomization mechanisms. We propose measures for disclosure risk from HA and derive closed-form relationships between privacy loss parameters in DP and disclosure risk from HA. We also provide a lower bound to the disclosure risk on a sensitive attribute when all the cells formed by quasi-identifiers are homogeneous for the sensitive attribute. The availability of the closed-form relationships helps understand the abstract concepts of DP and privacy loss parameters by putting them in the context of a concrete privacy attack and offers a perspective for choosing privacy loss parameters when employing DP mechanisms to release information in practice. We apply the closed-form mathematical relationships on real-life datasets to assess disclosure risk due to HA in differentially private sanitized frequency distributions at various privacy loss parameters.